Question

translate (3, - 3) to the left 2 units. then reflect the result over the x - axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point to the left

When translating a point \((x,y)\) to the left by \(a\) units, the new \(x\) - coordinate is \(x - a\) and \(y\) remains the same. Here, \(a = 2\), \(x=3\), \(y = - 3\).
The new \(x\) - coordinate is \(3-2=1\), and \(y=-3\). So the point after translation is \((1,-3)\).

Step2: Reflect the translated point over the \(x\) - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the rule is \((x,y)\to(x,-y)\).
For the point \((1,-3)\), after reflection over the \(x\) - axis, the \(x\) - coordinate remains \(x = 1\) and the \(y\) - coordinate becomes \(-(-3)=3\).

Answer:

\((1,3)\)